Ok, I finally managed to resurrect my Inkbook.
Initially, ArtaTech offered me a solution that didn't work (it was only available on Windows and seemed to use the same type of software than
rktools). I tried it on differents computers without success. So ArtaTech asked me to return the device to Poland, which was a bit expensive.
But they had provided me with a .zip that contained a .img file.
On a Linux computer, I followed the
instructions here. I had just to download the most recent version of
Linux upgrade tools here.
In order for it to work, I had to install adb for Android 4.2.2 and place the Inkbook in recovery mode (up right button + power button during some time). I don't know if it was important, but I typed "./adb reboot bootloader" before using Linux upgrade tools.
So it was quite a surprise to succeed !